[2015-2017] Signal processing with convolutional neural network FBPConvNet (2017) We concentrate on the relationship between iterative convex optimization framework and convolutional neural network. What is observed from LISTA approach is that unrolled scheme of iterative method is thought of as one kind of multi-layered neural network, furthermore, with the special property for normal operator (=convolution), we could link convolutional neural network with unrolled iterative shrinkage thresholding type reconstruction algorithms. [2014-2015] Signal processing in image processing [2014]-[2015] image inpainting algorithm using ALOHA We propose a patch-based image inpainting method using a low-rank Hankel structured matrix completion approach. The proposed method exploits the annihilation property between a shift-invariant filter and image data observed in many existing inpainting algorithms. In particular, by exploiting the commutative property of the convolution, the annihilation property results in a low-rank block Hankel structure data matrix, and the image inpainting problem becomes a low-rank structured matrix completion problem. The block Hankel structured matrices are obtained patch-by-patch to adapt to the local changes in the image statistics. To solve the structured low-rank matrix completion problem, we employ an alternating direction method of multipliers with factorization matrix initialization using the low-rank matrix fitting algorithm. As a side product of the matrix factorization, locally adaptive dictionaries can be also easily constructed. Despite the simplicity of the algorithm, the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state-of-the-art image inpainting methods. [2012-2015] Signal processing in Bio-imaging [2014]-[2015] accelerated MR imaging reconstruction algorithm using ALOHA Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Motivated by recent breakthroughs such as SAKE (simultaneous autocalibrating and k-space estimation) or LORAKS (Low-rank modelling of local k-space neighborhoods), an anni- hilating filter based low-rank Hankel matrix approach (ALOHA) is proposed as a general framework which unifies pMRI and CS-MRI as a weighted k-space interpolation problem. Our framework exploits an annihilating filter relationship originating from the sparsity in the transform domain as well as from parallel acquisition physics. This results in a rank-deficient Hankel structured matrix, whose missing data can be recovered with a low rank structured matrix completion algorithm after a k-space weighting. In particular, when the underlying image can be sparsified with a wavelet transform, the low rank matrix completion problem can be solved with a multi-scale pyramid resulting in efficient computation. Using the theoretical results from the latest compressed sensing literatures, we showed that the required sampling rates for ALOHA in both single and parallel imaging are nearly optimal. Experimental results with in vivo data for single/multi-coil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI. By reformulating the pMRI and CS-MRI as a weighted k-space interpolation problem that can be solved using a low rank Hankel structured matrix completion, the generalized ALOHA framework provides better insight into MRI reconstruction problems. [2013]-[2014] Generalized sampling interpolation in optical coherence tomography [2012]-[2014] Accelerated ultrasound imaging using data-driven dictionary learning and sparsity-penalized interpolation Ultrasound system needs massive the data storage for real-time video imaging. Until now, this bottleneck for saving large data is compensated by using beamforming performed on FPGA or DSP chip. Nowadays, compressed sensing (CS) theory demonstrated the undersampling framework showing better performance than Nyquist-Shannon sampling based on sparsity of representative coefficients in some domain. Applying the downsampling scheme in the raw meausrement (CS theory) of real-time dynamic B-mode ultrasound imaging, the accelerated ultrasound imaging using data-driven dictionary learning and sparsity-penalized interpolation without hardware chips(FPGA or DSP) can be proposed to reconstruct B-mode real-time ultrasonic images without the bottleneck of large memory space for raw measurements. [2008-2014] Terahertz & Optical systems [2012]-[2014] CW THz spectroscopy Frequency sweep is required for THz spectroscopy and tomography using continuous-wave (CW) radiation. While the frequency-modulated CW (FMCW) THz method can have a sweep rate as high as 10kHz, the frequency bandwidth is less than 100GHz. The photomixing method has a wide frequency range but needs a long measurement time with lock-in detection. In this project, experimental setup of THz frequency sweep at a high repetition rate is implemented. [2012]-[2014] THz reflection tomography using beam steering with telecentric f-theta lens Electronically controlled optical sampling (ECOPS) is combined with beam steering to demonstrate high-speed terahertz (THz) reflectoin three dimensional (3D) imaging. ECOPS is used for fast axial scanning and beam steering enhanced the speed of transverse scanning compared to moving a sample with translation stages. A telecentric f-theta lens is designed and fabricated for compensating distortions caused by beam steering. In this setup, the process of beam steering is conducted by two-axis galvanometer mirrors which are controlled by function generators. [2011]-[2012] High-speed THz reflection tomography We demonstrated high-speed terahertz (THz) reflection threedimensional (3D) imaging based on electronically controlled optical sampling (ECOPS). ECOPS enables scanning of an axial range of 9 mm in free space at 1 kHz. It takes 80 s to scan a transverse range of 100 mm × 100 mm along a zigzag trajectory that consists of 200 lines using translation stages. To show applicability of the imaging system to nondestructive evaluation, a THz reflection 3D image of an artificially made sample is obtained, which is made of glass fiber reinforced polymer composite material and has defects such as delamination and inclusion, and is compared with an ultrasonic reflection 3D image of the sample. [2010]-[2011] Spectrally encoding gradient imaging We suggested a new spectral imaging system using gradient encoding. The proposed system encodes the spatial information using the linearly and spatially distributed broadband spectrum illuminated to a 2-D target. The transmitted spectrum through sample is then focused to single point, whose spectrum is analyzed by a spectrometer. Due to the spatial encoding, we can then reconstruct the target sample using inverse Radon transformation. The concept of gradient encoding has been widely used for magnetic resonance imaging. We can easily implement this concept to 2D THz imaging system. [2008]-[2010] Compressed sensing THz reflection tomography We demonstrated a “pulse-echo” mode T-ray tomography, where a transmit antenna transmits a THz pulse and the receiver antenna on the same side measures the THz waveforms. Thanks to sufﬁcient incoherency of the sensing matrix, the acquisition time can be signiﬁcantly reduced without sacriﬁcing its resolution if the image targets are sparsely distributed or compressible using compressed sensing theory. Furthermore, an asynchronous optical sampling THz-TDS technique can replace the mechanical delay stage with optical sampling using two phase locked lasers, further accelerating the acquisition of accurate waveform measurements. |

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